Chapter 5: Interpreting Fractions In The Classroom

Today we will be learning about place value. When we divide numbers with three and four digits by a one digit number, the quotient doesn’t always go about the first number in the dividend like we saw yesterday. This is important to know because if you had to split $100 with your sister and you divided $100 by 2 and placed the 5 above the 1, then added two zeros, you would have to pay your sister $500. That’s not dividing, or fair. Remember we need to know how to divide so you can evenly split something, like money.”

Students had previously covered the topic of developing fluency in multiplication by 2-digit numbers. After that topic students moved on to cover number sense, dividing by 1-digit divisors using mental math to prepare them for the following topic of my learning segment. The topic of my learning segment consists of developing fluency, dividing by 1-digit divisors. I designed my lesson as a three-day unit focusing on long division by modeling division with place-value blocks, dividing 2-digit by 1-digit numbers, and dividing 3-digit by 1-digit numbers. Students were introduced to division prior to my learning segment but the struggled to understand and comprehend division because students were only introduced to the division algorithm and were not provided with a mnemonic to help them recall the steps. Students also weren’t introduced to division with manipulatives or drawings. Therefore, I

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

In the chapter, “Equal Sharing Problems and Children’s Strategies for Solving them” the authors recommend fractions be introduced to students through equal sharing problems that use countable quantities because they can be shared by people or other groupings. In other words, quantities can be split, cut, or divided. Additionally, equal sharing problems assist children to create “rich mental models “for fractions (p.10).

Montana is working towards using effective strategies for comparing fractions. She identified that 2/4 and 4/8 were ‘both halves, therefore, the same’ (equivalent fractions); she used a

Once students get to the fourth grade, learning equivalence in fractions with unlike denominators is something that they can look forward to...or not look forward to. It can be a very tough lesson and something that is hard for the children to understand. They need to have a simple understanding of fractions already. They need to know what they are and how they add up together. Meaning that they need to understand that fractions are a part of a whole...a fraction of something, and that if the fractions are equal they can add up to create a whole. The easiest way to describe this and review it is with a circle representing a pie. Each slice comes from the pie and all put together its a whole. Also the stronger the students is with their

Math is all around us. Everywhere you go there is some sort of math involved consciously or subconsciously. Even though math is all around us, and everything we do involves math, I myself must say I dislike math. Research has shown there are many more people that dislike math compared to those who do like it. A survey done by a nonprofit organization named Change the Equation asked 1,000 middle school kids in 2010 whether they would prefer to eat broccoli or do one math problem, surprisingly more than half answered they would eat broccoli. Throughout the years, there have been many different strategies created on how to introduce and/or teach math to children.

Goal: At the end of the lesson the students will be able to evaluate twenty five fraction problems, and some of the fraction problems will include word problems

I would with one students on how to make equivalent fractions, She was very confused and did not know how. So I demonstrated the example that was written on the board. I wrote 3/6 and then wrote the division character by the numerator and denominator and then wrote 3. So then I said 3/3=1 and 6/3=2, then wrote 1/2. Then we tried to reduce 25/100, so I said, “What can you divide by 25 and 100.” She said 5 so she followed the example that I had written. So I said, what’s 100/5, she said, 20. So we knew the denominator was 20. Then I said whats 25/5, she said 5. So then I said the equivalent fraction is 5/20. She wrote done all that we had discussed above as we were finding the answer. I still think she was a little confused after, but it was time for discussion. For next time, I think I would try multiplying as another example, which I think could help the student see both. what I would have done was try multiplying instead of

The pre-assessment used to establish students' baseline knowledge and skills for this lesson was a comparing fractions pre-test. Students compared the following types of fraction comparisons: unit fractions, benchmark fractions, normal fractions, equivalent fractions, improper fraction vs. normal fractions, and improper vs. improper fractions. I have taken the information and used it to figure out which types of comparisons the students understand and using it to work on increasing the students' ability to include the other types. I use the information to accommodate what the students already know about the target. It showed me that students do not understand how to compare fractions, when they have a different denominator.

In math we are supposed to learn or memorized plenty of formulas and compute them. In the video Why is Math Different Now by Dr. Raj Shah he talks about “how in math we give children standard algorithms, but we don’t understand where these numbers are coming from” (Shah). He provides an example by using two digit numbers multiple by two digit numbers. In this example he is saying how children do not understand the place values and where the extra zero is coming from, but in this new way of doing multiplication it shows the place values and where the zeros are coming from. This helps children understand the problem and not just getting the right answer like we have been doing in the past. The old method does not let students think freely or creatively. This approach helps children understand the number and just not worry about getting the right

Learning about the long and tiresome process of transforming ordinary fractions into decimal fractions has made me realize how much I had taken for granted using calculator for the past decade. There are downsides to relying more on the calculator than relying on “old-fashioned” mind. “Patterns as Aids” becomes a problem when a student follows rules without understanding and calculates large numbers mentally using tricks but fails to understand the purpose of the processes or steps. Therefore it is better to understand less but thoroughly, than to be an expert in memorizing tricks and rules without any understanding. Principles must be taken apart, and each ingredient learned and taught individually. When something sounds hard or difficult, it usually means we did not break the problem into portions. Often I take for granted and overlooked simple aspects of math that I automatically perform. This book also mentions the importance of using word

As a future teacher, I think this concept is important because we use the basic conversions in our daily lives. The second main idea is Volume. Volume is cubed the units of measurement are: ounces, cup, pint, quart, and gallon. There is 8 ounces in a cup, 2 cups in a pint, 2 pints in a quart, and 4 quarts in a gallon.

Upon observing a 6th grade math class I observed the teacher teaching the student’s about order of observation to evaluate algebraic expression. On the following day the teacher introduced the students into the concept of translating math phrases into numbers, variables, and operations. At the completion of my class observation I was able to administer a formative assessment on ratios. This paper will document what was observed during the ratio assessment.

The first lesson observed shows Christie Kawalsky (Christie) at St. Albans East Primary School teaching fractions to a Year 3 class (Australian Institute for Teaching and School Leadership [AITSL] (Producer). (n.d.-a).